CHANDRAX-ray Center 60 Garden St., Cambridge Massachusetts 02138 USA

MEMORANDUM

Date: Jun 23, 2004From: T. J. GaetzTo: FileSubject: Analysis of the Chandra On-Orbit PSF WingsFile: wing analysis.tex

Version: 1.0-Rev1 (Jul 18, 2008)

Abstract

This memo presents an analysis of the wings of the Chandra point spread function(PSF). The PSF wings result from X-ray scattering from microroughness on the sur-faces of the optics. The wings are very faint compared to the direct specular image.In order to study the wings, a deep observation of a very bright high latitude X-raysource (Her X-1, ObsID 3662) is analyzed. Radial profiles are extracted in two ways:In one analysis, the mirror effective area at the position of the specular image is used;this is appropriate for investigating the intrinsic HRMA PSF. The second analysis usesa more conventional exposure map. Radial profiles are extracted, and normalized by aspectrum extracted from the ACIS transfer streak. The profiles are fit to exponentiallytruncated power laws (with a spatially constant term to model detector background),and the resulting fit coefficients are tabulated.

Pileup metrics are examined, and to be conservative, the fits are restricted to θ>∼15′′.The pileup in the ACIS transfer streak is estimated to be 4%.

Because the mirror scattering is in part diffractive, the diffuse mirror scatteringhalo is energy dependent; high energy photons tend to be scattered to larger anglesthan low energy photons. This spectral hardening is also examined.

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Contents

1 Introduction 4

2 The Observation 6

3 Data Reduction 7

3.1 Radial Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Normalizing the profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 ANALYSIS 10

4.1 Pileup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2 Preliminary Powerlaw Fits . . . . . . . . . . . . . . . . . . . . . . . . . . 104.3 Powerlaw plus Exponential Cutoff Fits . . . . . . . . . . . . . . . . . . . 11

5 Summary and Caveats 17

6 References 20

A Pileup 21

B The ACIS Transfer Streak 25

B.1 Estimating the Transfer Streak Spectrum . . . . . . . . . . . . . . . . . 25B.2 Evaluating the Her X-1 Transfer Streak Spectrum . . . . . . . . . . . . 26B.3 Pileup in the Her X-1 ACIS Transfer Streak . . . . . . . . . . . . . . . . 29

C Exposure Correction and Effective Area 29

D Fits Including Mirror Vignetting 31

E Diffuse PSF Wings: spectral variations 38

F Anomalous 1.5 keV line feature 43

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List of Tables

1 Summary of the Observation . . . . . . . . . . . . . . . . . . . . . . . . 62 Fit Parameters. (Note: errors are purely statistical.) . . . . . . . . . . . 13D.1 Fit Parameters. (Note: errors are purely statistical.) . . . . . . . . . . . 32

List of Figures

1 Schematic of PSF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Derolled Her X-1 wings observation. . . . . . . . . . . . . . . . . . . . . 73 Annotated closeup of the Her X-1 wings observation. . . . . . . . . . . . 84 Powerlaw index for fits to narrow-band Her X-1 profiles. . . . . . . . . . 115 Fits for 1.0-2.0 keV and 2.0-3.0 keV. . . . . . . . . . . . . . . . . . . . . 146 Fits for 3.0-4.0 keV and 4.0-5.0 keV. . . . . . . . . . . . . . . . . . . . . 157 Fits for 5.0-6.0 keV and 6.0-7.0 keV. . . . . . . . . . . . . . . . . . . . . 168 Fits for 7.0-8.0 keV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 Variation in local powerlaw slope. . . . . . . . . . . . . . . . . . . . . . . 18A.1 Ratio of ASCA “bad” grades to ASCA “good” grades; subassembly data

and on-orbit background. . . . . . . . . . . . . . . . . . . . . . . . . . . 22A.2 Her X-1 profiles of bad vs. good grades. . . . . . . . . . . . . . . . . . . 23A.3 Her X-1 profiles of grade 0 vs. grade 6. . . . . . . . . . . . . . . . . . . . 24B.1 Schematic of the transfer streak calculation. . . . . . . . . . . . . . . . . 27D.1 Fits for 1.0-2.0 keV and 2.0-3.0 keV (conventional exposure map). . . . . 33D.2 Fits for 3.0-4.0 keV and 4.0-5.0 keV (conventional exposure map). . . . . 34D.3 Fits for 5.0-6.0 keV and 6.0-7.0 keV (conventional exposure map). . . . . 35D.4 Fits for 7.0-8.0 keV (conventional exposure map). . . . . . . . . . . . . . 36D.5 Variation in local powerlaw slope. . . . . . . . . . . . . . . . . . . . . . . 37E.1 Her X-1 transfer streak spectrum. . . . . . . . . . . . . . . . . . . . . . . 38E.2 Her X-1 diffuse scattering wings, 10′′−15′′, 15′′−20′′, 20′′−30′′, 30′′−40′′. 39E.3 Her X-1 diffuse scattering wings, 40′′−60′′, 60′′−80′′, 80′′−120′′, 120′′−

160′′. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40E.4 Her X-1 diffuse scattering wings, 160′′ − 220′′, 220′′ − 280′′, 280′′ − 340′′,

340′′ − 400′′. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41E.5 Spectra of diffuse scattered wings . . . . . . . . . . . . . . . . . . . . . . 42F.1 Powerlaw index for fits to the narrow band obsid 3662 data. . . . . . . 43F.2 Her X-1 diffuse wings spectrum (160−220′′) and transfer streak spectrum. 44

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1 Introduction

The PSF of the Chandra High Resolution Mirror Assembly (HRMA) includes con-tributions ranging from nearly specular reflection from low frequency figure errors (the“core” of the PSF) to scattered photons reflecting/diffracting off of surface microrough-ness on the optics (the “wings” of the PSF). The scattered photons form a faint diffusehalo extending to large angles. The Chandra on-axis PSF can thus be approximatelydivided into two limiting regimes (see Fig. 1):

• core, consisting of quasi-specular X-rays reflecting from the mirror surface (in-cluding the effects of low-frequency mirror figure errors, deformations, and mis-alignments)

• wings, consisting of reflected/diffracted X-rays which scatter off the high spatialfrequency components of the surface. The wings are energy dependent. The on-axis azimuthally-averaged wing profile falls approximately as θ−γ, where θ is theangular distance from the core and γ ∼ 2.

SB10

log

(arcsec)θ10

log

quasi−specular reflection from low−freq surface errors

CORE

)−2θ∼(diffraction from surfacemicroroughness

WINGS

heavily piled

unpiled

piled up

background

SB10

log

(arcsec)θ10

log

Figure 1: Left: Schematic of the on-axis PSF as a function of angular distance fromthe core. Right: Schematic of the effects of detector pileup and background.Count rate per pixel above some limit results in pileup. The pileup modifiesthe event grades (“grade migration”), which for serious enough degradation,results in loss of the event. Detector and sky background limits how low thesource count rate per pixel can be detected.

In order to better understand the PSF and the wings as a function of energy, on-orbit data using ACIS as the detector is needed. Because of detector pileup, ACIShas a relatively limited dynamical range. The detector evaluates event positions andenergies based on the charge detected within 3 × 3 pixel islands. If more than one

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event contributes significant charge to an island within the frame accumulation time(typically 3.2 seconds), the energy of the detected event is perturbed; with severepileup, the event is no longer detected as a valid X-ray event. This presents formidableproblems for studying the PSF. The core of the Chandra PSF is very narrow (subpixel)and its study requires very faint sources in order to avoid pileup. The far wings are veryfaint compared to the core: a very bright source is needed in order to see the wings withgood statistics above the detector background, but this results in heavy pileup in thecore and inner wings, complicating the assessment of the intrinsic source rate. Whenusing astronomical sources, great care is also needed to avoid building astrophysicsinto the calibration. For example, any intervening dust column will scatter X-rays andproduce an X-ray dust scattering halo. Cosmic dust scattering is most important atlow energies; the total dust-scattered power scales roughly as E−2, but at fixed angle,the amplitude scales very roughly as E−1. In order to minimize the effects of dusthalos, it is necessary to use sources with as low an NH column as possible. Anotherpotential contaminant is diffuse emission such as emission from the galaxy hosting anactive galactic nucleus (AGN). Consequently, the most promising candidates are stellarsources and compact objects at high galactic latitude.

In this memo, an analysis of the Chandra wings based on a deep observation ofHer X-1 (ObsID 3662) is presented. Some aspects are preliminary. In particular, theACIS optical blocking filters have a nonuniform contamination layer which reduces theeffective quantum efficiency (QE) of the detector in a spatially and energy dependentmanner. The effect of this contamination is most significant for low energies, andnegligible at high energies. Because of this, there remain uncertainties in the PSF wingprofiles and normalization below ∼ 1 keV. Investigations of the azimuthal dependenceof the wings have also been postponed.

The organization of this memo is as follows. In §2, the Her X-1 observation (ObsID3662) is described. The data reduction, extraction of radial profiles, and treatmentof the effective area and exposure correction are discussed in §3. In §4 the analysisof the profiles is discussed. The core and inner wings for this observation are heavilypiled up, so to be conservative, the profile fits are performed only for radii >∼15′′;pileup estimation for the wings and for the transfer streak is discussed in Appendix A.The profiles are fitted using powerlaws with an exponential cutoffs, and plots and fitparameters for the wings in broad energy bins (∆E = 1 keV) are provided. Thesefits are to profiles constructed without including mirror vignetting in the exposurecorrection; see Appendix C for a discussion. The corresponding fits with the mirrorvignetting included are provided in Appendix D. The profiles are normalized usingthe spectrum extracted from the ACIS transfer streak from the core and scaling forthe frame transfer duty cycle; the normalization calculations are discussed further inAppendix B.1. In §5, the main features of the analyses are summarized, and caveatson the interpretation are discussed.

Because the mirror scattering is in part diffractive, the scattering angle dependson energy - for a given roughness and angle of incidence, high energy photons willscatter to larger angles than low energy photons. Consequently, the diffuse mirrorscattering wings tend to harden with increasing angle from the core; this is discussedin Appendix E where spectra extracted from concentric annular regions are presented.

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Finally, Appendix F discusses the anomalous line feature near 1.5 keV in the diffusespectrum at large radii; its origin is unknown, but it is believed to be a telescopeartifact, possibly resulting from the extremely bright source and the configurationused.

2 The Observation

In order to calibrate the far wings of the PSF, Her X-1 was observed. Her X-1 was selected because it is a very bright source (in its high state) at high galacticlatitude (b = 37.52), with low extinction (E[B − V ] < 0.05; see Liu et al. (2000)). Thetotal galactic column in that direction is NH ∼ 1.8 × 1020 cm−2 (Dickey & Lockman,1990). The total X-ray cosmic dust scattering halo is likely . 1.5% (Smith et al.,2002). Her X-1 was observed by Chandra for 50 ks on July 1-2, 2002, imaged on acorner of the ACIS S3 chip with the detector translated to place the image ∼ 45′′ fromthe optical axis (see Fig. 2). Although the source is somewhat off-axis, this does notsignificantly affect the far wings — 0.75′ is much smaller than the mean graze angleof the smallest mirror pair (∼ 27′). The ACIS I2, I3, and S2 chips were also on toprovide additional coverage. The nominal ACIS frame time was 3.1 seconds. The VeryFaint (VF) Timed Exposure (TE) mode was used, although the current study doesnot apply VF filtering. The radiation environment was quiescent (no flares) and thebackground, evaluated for 11–13 keV, was 4.83% higher than that for the appropriateblank sky background dataset (acis7sD20001201bkgrndN002.fits).

Table 1: Summary of the Observation

ObsID Object Exposure Frame Time θ NH ( cm−2)Wings 3662 Her X-1 high state 50 ks 3.1 s 45′′ 1.8 × 1020

In Fig. 3, part of the derolled image of the Her X-1 ObsID 3662 observation isplotted, with the ACIS transfer streak and the strut shadows indicated. The strutshadows are caused by the mirror support struts. The presence of these shadowsindicates that the diffuse halo is predominantly caused by in-plane mirror scatteringrather than a diffuse astrophysical halo due to dust scattering along the line of sight.The image of a diffuse astrophysical halo would be the superposition of many imageslike Fig. 3 which would tend to fill in the shadows. A portion of the azimuthal profile(1–2 keV, 1′–2′ from the source, 1◦ bins in azimuth φ) is shown in right panel of Fig. 3.The depth of the shadows indicate that any cosmic dust halo contribution cannot bemore than ∼ 1/4 of the observed halo, confirming that the diffuse halo is primarilycaused by mirror scattering.

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Figure 2: Derolled image of the Her X-1 wings observation, ObsID 3662. The eventlist was energy filtered (0.5-2.0 keV) to reduce the background. The white‘+’ indicates the location of the nominal optical axis during the observation.

3 Data Reduction

The data were reprocessed without pixel randomization, starting with the level 1event lists. In this initial analysis, I consider ACIS-S3 data only. Very Faint filteringis not applied at this time.

Ultimately, extracting the PSF is a combined spatial/spectral problem: one wantsthe spatial profile of the wings as a function of energy. Unfortunately, there do notcurrently exist tools to deal easily with a combined spatial/spectral analysis. Theapproach I have taken is to construct narrow-band count images. The bands are∆E = 0.1 keV for 0.4–2.2 keV, ∆E = 0.2 keV for 2.2–8.0 keV, and ∆E = 0.5 keVfor 8.0–10.0 keV. For the same energy bins, dithered QE maps are constructed using

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strut shadows

ACIS transfer streak

Figure 3: Left: Closeup of the deep Her X-1 wings observation. The ACIS transferstreak results from photons hitting the detector during the frame transferto the frame store. The observation is notable for showing the shadowsproduced by the mirror support struts. Right: azimuthal variation of the0.5–2.0 keV diffuse emission 1–2′ from the source; 1◦ bins in φ.

the CIAO1 tools mkinstmap to construct the QE map and mkexpmap to project theQE map to the sky, including the effects of dither. In using mkinstmap, the HRMAeffective area is excluded, resulting in effective QE maps rather than conventionalexposure maps (see Appendix C for a discussion; the alternative approach of includingthe mirror vignetting in the exposure map calculation is presented in Appendix D).The mirror effective area is evaluated separately for a small (10′′ radius) region centeredon the position of the specularly imaged source. Exposure-corrected images are thenformed by dividing the counts images by the dithered QE maps, the total exposuretime, the effective area at the source position, and a correction for the low-energy QEdegradation (see Eq. 1). These corrected images are combined into broader (1 keVwide) band images; the sum is weighted to account for an approximate treatment ofthe energy-dependence of the low energy QE degradation from the ACIS contaminant.

For ObsID 3662, the effect of background is evaluated using the appropriate blanksky background data (acis7sD20001201bkgrndN002.fits) obtained from the Chandra

calibration database2. The sky background dataset is reprojected to the sky using

1CIAO is a set of analysis tools produced by the Chandra X-ray Center.See http://cxc.harvard.edu/ciao/.

2http://cxc.harvard.edu/caldb/

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the CIAO tool reproject events with the ObsID 3662 aspect solution. Narrow-bandcounts and dithered QE maps are constructed, and exposure-corrected images areconstructed in the same way as for the wings data. As noted in §2 the radiation envi-ronment was quiescent; based on comparing the rates for 11–13 keV, the backgrounddataset is rescaled by 1.0483.

3.1 Radial Profiles

Radial profiles are extracted using annular regions centered on the source. The ra-dial binning is variable: the inner bins are defined as θi = θi−1 +∆θ where ∆θ = 2′′, butbeyond 20′′, the radii increase faster than linearly as θi = 1.1 × θi−1 . Asymptotically,this provides approximately logarithmic binning. For logarithmic binning, a powerlaw∝ θ−2 would produce approximately the same number of source counts in each bin (al-though the included background counts would be increasing with radius). Extraneoussources are excised from the annular regions, and the regions are also clipped near chipboundaries (allowing for the extent of the dither pattern). The ACIS transfer streakfor the bright central source significantly contaminates the profile at large θ. A narrow(10 pixel wide) rectangle centered on the streak is therefore excised.

For each energy band, radial surface brightness profiles are constructed from thecounts image and from the QE and exposure corrected images; the counts image dataare used to propagate errors for the QE and exposure-corrected data. This results insurface brightness profiles for the quantity

〈ψsrc〉∆θi=

〈Csrc,corr 〉∆θi

Aeff ,src tsrc,exp(1)

where Csrc,corr = Csrc,counts/qQ is the QE-corrected counts image, Aeff is the effectivearea at the source position (see Appendix C), texp is the exposure time, and q is a(spatially independent) correction factor for the low-energy QE degradation at thetime of the observation (≃ 1 for E>∼1). The 〈〉∆θi

indicates an average over annulus iof width ∆θi and also over the energy band ∆E.

The surface brightness for background is constructed in the same way using the skybackground dataset:

〈ψbgd〉∆θi=

〈Cbgd ,corr 〉∆θi

Aeff ,src tbgd ,exp

(2)

For consistency with the source profile calculation, the effective area at the source, Aeff

is used. The correction factor, q, for the low energy QE degradation is not applied forthe background (predominantly charged particle events).

3.2 Normalizing the profiles

The treatment outlined in §3.1 still includes the underlying spectrum of the source.The surface brightness therefore needs to be normalized. Ideally one would use theintegral over the PSF profile out to some fiducial distance. In the case of the deepwings observation, almost all of the directly imaged photons are lost to extreme pileup

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in the core with grade migration into bad events, so an alternative approach must befound. An attempt was made to match the profile to a zero-order HETG grating imageof the source in a low state. Unfortunately, the profile obtained for this ACIS/HETGobservation disagrees significantly with a deep HRC-I observation of AR Lac (Gaetzet al. 2003 Chandra Calibration Workshop Presentation)3. A stack of observations offaint sources (mostly HETG grating zero order images) also shows this effect (Jerius et

al. 2003 Chandra Calibration Workshop Presentation)4 Currently, the normalizationderived from the ACIS transfer streak is believed to be more reliable than matchingprofiles, although some properties of the transfer streak properties remain uncertain.In the following, a normalization based on the transfer streak spectrum is used. Thenormalization calculation is discussed further in Appendix B.

4 ANALYSIS

4.1 Pileup

Because of the extreme brightness of the source, the central regions of the profileare heavily piled up, and we need to know how far out the profile is affected by pileup.Several approaches for assessing pileup are discussed in Appendix A; based on thesepileup diagnostics, I estimate that pileup is significant inside a radius of ∼ 8′′, andpossibly as far as ∼ 15′′. Although radial profiles may be extracted for radii < 15′′, tobe conservative, only data for ≥ 15′′ are included in the fits.

4.2 Preliminary Powerlaw Fits

The first stage of the analysis is to fit powerlaw profiles to the radial profiles ex-tracted for the narrow-band Her X-1 wings data:

ψ(θ) = a

[

θ

θ0

]

−α

+ b (3)

where b is the background component, a is the wing amplitude scale factor, α is thepowerlaw slope, and θ0 ≡ 10′′ is a reference radius. These are simultaneous fits to apowerlaw plus constant background to both the Her X-1 dataset and the correspondingblank sky background dataset; the powerlaw amplitude is frozen at 0 in the backgrounddataset fits.

The powerlaw slopes are plotted as a function of energy in Fig. 4. The profiles aresteep at low energies, rapidly becoming shallower toward ∼ 1.8 keV. Below ∼ 1 keV,the low-energy QE degradation is very important; an approximate correction has beenapplied, but the magnitude and spatial nonuniformity of the effect are still underinvestigation. Consequently, the derived powerlaw indices for E . 1 keV are somewhatuncertain. The powerlaw slope is fairly constant for ∼ 1.8–5.0 keV, and steepens again

3http://cxc.harvard.edu/ccw/proceedings/index.html/presentations/gaetz/index.html4http://cxc.harvard.edu/ccw/proceedings/index.html/presentations/jerius/index.html

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above ∼ 5 keV. The steepening above 5 keV is likely the result of the roughest mirrorpair (MP1) dropping out as its effective area rapidly declines with increasing energy.

Because of pileup effects, the wings are fit only for θ ≥ 15′′. The radial profilesfor the Her X-1 dataset are fit simultaneously with profiles extracted from the skybackground dataset; the background contribution is fit as a constant.

??

Steeper at low E

Roughest mirror drops out

Figure 4: Powerlaw index for fits to the narrow band ObsID 3662 data. See text andAppendix F for further discussion of the “glitch” near 1.5 keV.

In examining the powerlaw slopes more carefully, a glitch in the trend was notedat 1.5 keV. Further investigation uncovered an anomalous line feature in the diffuseemission at 1.5 keV which does not appear in the background spectrum or in a spectrumextracted from the transfer streak. This feature is believed to be a telescope artifact,although its origin is not currently understood. This analysis is discussed further inAppendix F. The 1.4–1.6 keV region was removed from the analysis and the bandfilled by interpolating from the adjacent energy bands.

4.3 Powerlaw plus Exponential Cutoff Fits

To improve the statistics in the profiles, the very narrow band data were combinedinto 1 keV bands and fit in the same way as in §subsec:fitting.the.profiles. These profiletend to be shallower than the best fit powerlaw at smaller angles, and steeper at largeangles. In order to allow for this behavior, the wing profile is fit by a powerlaw plusexponential cutoff plus spatially constant background:

ψ(θ) = a

[

θ

θ0

]

−α

exp (−cθ) + b (4)

where b is the background component, a is the wing amplitude scale factor, α is thepowerlaw slope, and 1/c is the exponential cutoff scale length. The fit is scaled to

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a reference radius, θ0 ≡ 10′′. The background datasets are fit with the a parameterfrozen at 0. The resulting fits are plotted in Figs. 5-8.

For comparison, models based on the ground calibration data are overplotted.5

Above ∼ 2 keV and beyond ∼ 15− 20′′, the profiles are reasonably consistent with themodel constructed based on ground calibration data. The on-orbit wings tend to havea slightly shallower slope, consistent with expectations: in the ground experiments, thenonuniform illumination undersampled the rougher ends of the optics, and the rougherregions would be expected to scatter more. The profiles for the ground data show anupward curvature toward smaller θ which is not seen in the on-orbit profiles. Althoughpileup becomes significant as the core of the PSF is approached, it does not seemsufficient to explain the differences ∼ 10 − 20′′ from the core. Ground measurementsof the wings were not obtained for the HRMA as a whole. Instead, the model is basedon combining data for individual quadrants of individual mirror pairs at a sparse setof energies into “Power Spectral Densities” (PSDs; functions of spatial frequency ofthe surface microroughness). The four individual PSDs (one for each mirror pair)are combined into a surface brightness profile, taking into account the photon energy,the mean graze angle for each mirror pair, and weighted by the fractional effectivearea. The steepening in the model originates in the models for the inner two mirrorpairs; it may be an artifact of the fitting process and systematics in the data and ofvarious stages of the analysis. Based on current understanding, it is believed that thetrue wings for E<∼20′′ are intermediate between the on-orbit estimate and the ground-based estimate, but likely closer to the on-orbit value. However, pileup (increasinglyimportant in this dataset inside ∼ 10− 15′′ would have the effect of reducing the slopetoward smaller radii.

5See memo: http://cxc.harvard.edu/cal/Hrma/psf/XRCF PSF wing profile/

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Chandra

PSF

Win

gs

Table 2: Fit Parameters. (Note: errors are purely statistical.)

Energy γ a c b χ2(dof)(keV) (ct s−1 arcsec−2) (arcsec−1) (ct s−1 arcsec−2)1.0-2.0 1.972 ± 0.003 (0.748 ± 0.004) × 10−05 (0.675 ± 0.049) × 10−03 (0.373 ± 0.003) × 10−08 246(70)2.0-3.0 1.840 ± 0.004 (1.012 ± 0.007) × 10−05 (1.212 ± 0.060) × 10−03 (0.525 ± 0.004) × 10−08 70(70)3.0-4.0 1.760 ± 0.008 (1.875 ± 0.016) × 10−05 (1.963 ± 0.052) × 10−03 (0.661 ± 0.007) × 10−08 104(70)4.0-5.0 1.749 ± 0.008 (2.569 ± 0.022) × 10−05 (1.982 ± 0.051) × 10−03 (0.840 ± 0.009) × 10−08 75(70)5.0-6.0 1.902 ± 0.011 (3.471 ± 0.037) × 10−05 (1.783 ± 0.074) × 10−03 (1.406 ± 0.015) × 10−08 133(70)6.0-7.0 1.948 ± 0.015 (4.017 ± 0.059) × 10−05 (1.844 ± 0.116) × 10−03 (3.177 ± 0.030) × 10−08 98(70)7.0-8.0 2.137 ± 0.030 (4.909 ± 0.128) × 10−05 (−0.333 ± 0.253) × 10−03 (16.605 ± 0.116) × 10−08 121(70)

13/

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Chandra

PSF

Win

gs

Figu

re5:

Pow

erlawplu

sex

pon

ential

cutoff

fits

toth

eob

sid3662

(Her

X-1

win

gs)data;

the

fits

were

forθ≥

15′′.

The

model

based

ongrou

nd

calibration

data

isalso

indicated

(labeled

“xrcf”).

Top

:1.0-2.0

keV.

Bottom

:2.0-3.0

keV.

14/

44

Chandra PSF Wings

Figure 6: Powerlaw plus exponential cutoff fits to the obsid 3662 (Her X-1 wings) data;the fits were for θ ≥ 15′′. The model based on ground calibration data isalso indicated (labeled “xrcf”). Top: 3.0-4.0 keV. Bottom: 4.0-5.0 keV.

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Chandra PSF Wings

Figure 7: Powerlaw plus exponential cutoff fits to the obsid 3662 (Her X-1 wings) data;the fits were for θ ≥ 15′′. The model based on ground calibration data isalso indicated (labeled “xrcf”). Top: 5.0-6.0 keV. Bottom: 6.0-7.0 keV.

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Chandra PSF Wings

Figure 8: Powerlaw plus exponential cutoff fits to the obsid 3662 (Her X-1 wings) data;the fits were for θ ≥ 15′′. The model based on ground calibration data isalso indicated (labeled “xrcf”). 7.0-8.0 keV.

Because of the form of the fit, the local powerlaw slope varies as a function ofenergy and θ, illustrated in Fig. 9. The asymptotic slope is steepening with energy;the highest energy bin (7–8 keV) has poor statistics at large radii, and the shape of theprofile is relatively poorly constrained. For the energy bins below 7 keV, the curvatureof the profile increases up to ∼ 4–5 keV, then stays relatively constant, but with theoverall slope very gradually steepening.

5 Summary and Caveats

The deep observation of Her X-1 (ObsID 3662) provides the most detailed infor-mation available on the on-orbit (nearly) on-axis wings of the Chandra PSF. In thepresent study, the wings are examined for relatively broad energy bands (∆E = 1 keV)so that the wings can be followed with good statistics to large distances from the spec-ular image. For E ≤ 7 keV, the profiles can be followed out to ∼ 8′; beyond 8′, thestatistics for the S3 profiles deteriorate rapidly as the surface brightness falls and alarger fraction of each annulus falls off the detector. As can be seen in Fig. 8, the pro-file can be followed out to at least 5′ even for for the 7–8 keV band (although the poorstatistics for the 7–8 keV do not provide very good constraints on the profile shape).

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Chandra PSF Wings

Figure 9: Variation in local powerlaw slope. The curves are labeled by the value of θ inarcsec. The highest energy band (7–8 keV) is poorly constrained; the flatterprofile is likely influenced by uncertainties in the background subtraction.

The additional data on S2, I2, and I3 may allow the profile to be probed further out.The data are analyzed by constructing narrow band counts images and normaliz-

ing them using a dithered QE map and the mirror effective area and vignetting at theposition of the specular image of Her X-1. (An alternative treatment using a more con-ventional exposure map which includes mirror vignetting at the detected event positionis included as Appendix D; see Appendix C for further discussion.) An approximatetreatment of the low energy QE degradation resulting from the ACIS contaminationis included, but this includes only the spectral distribution and does not contain thespatially dependent component; the effect of the spatially-dependent contaminationcomponent is negligible at high energies, but is an important effect below ∼ 1 keV,and becomes increasingly important as energy decreases.

The extracted radial profiles are fit by a powerlaw with an exponential cutoff anda spatially constant background term (Eq. 4). Profiles for the Her X-1 observation,and corresponding profiles for a blank-sky dataset are fit simultaneously; the profilesfor the blank sky data are rescaled upward by 4.8%, based on comparing the Her X-1ObsID 3662 data and the blank sky data for 11–13 keV.

The fits are for 1 keV wide bands from 1-2 keV to 7-8 keV. Below 1 keV the results

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are very uncertain because of the energy and spatial dependence of the absorptionfrom the contamination layer on the ACIS optical blocking filter. Above 7–8 keV, thestatistics rapidly become poorer. The fits parameters are listed in Table 2 and thefits are plotted against the data in Figs. 5-8; for reference, model based on groundmeasurements6 are also plotted. (The corresponding parameters and plots for profilesderived using a more conventional exposure map given in Table D.1 and Figs. D.1-D.4.)

Above ∼ 2 keV and beyond ∼ 15 − 20′′, the profiles are reasonably consistentwith the model constructed based on ground calibration data. The on-orbit wingstend to have a slightly shallower slope, consistent with expectations: in the groundexperiments, the nonuniform illumination undersampled the rougher ends of the optics,and the rougher regions would be expected to scatter more. The profiles for the grounddata show an upward curvature toward smaller θ which is not seen in the on-orbitprofiles. Although pileup becomes significant as the core of the PSF is approached, itdoes not seem sufficient to explain the differences ∼ 10 − 20′′ from the core. This isbelieved to result from artifacts and systematic errors in combining the ground data.

Based on current understanding, it is believed that the true wings for E<∼20′′ areintermediate between the on-orbit estimate and the ground-based estimate, but likelycloser to the on-orbit value. However, pileup (increasingly important in this datasetinside ∼ 10 − 15′′) would have the effect of reducing the slope toward smaller radii.

The normalization of the profiles is also subject to systematic errors. In order toput the profiles on the same footing so that they can be directly compared (and scaled),the surface brightness should be scaled by the total exposure-corrected count rate ofthe source over the corresponding energy band. Because of extreme pileup, removesmost of the directly imaged photons are lost, a direct estimate of the count rate are notavailable. In this memo, the profiles have been normalized using a spectrum extractedfrom the events accumulated during ACIS frame transfer. The frame transfer time ismuch shorter than the frame accumulation time, so the transfer streak events are muchless susceptible to pileup; in this observation, the QE degradation for transfer streakevents is estimated to be ∼ 8%. In addition, no aperture correction for the pileupextraction region has been applied to account for the PSF wing contribution fallingoutside the narrow (10′′-wide) transfer streak extraction region. This is estimated tobe at most a 5–10% effect.

6http://cxc.harvard.edu/cal/Hrma/psf/XRCF PSF wing profile/

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6 References

References

Dickey, J. M. & Lockman, F. J. 1990, ARA&A, 28, 215

Heinke, C. O., Edmonds, P. D., Grindlay, J. E., Lloyd, D. A., Cohn, H. N., & Lugger,P. M. 2003, ApJ, 590, 809

Liu, Q. Z., van Paradijs, J., & van den Heuvel, E. P. J. 2000, A&AS, 147, 25

Smith, R. K., Edgar, R. J., & Shafer, R. A. 2002, ApJ, 581, 562

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A Pileup

If two or more events within a single frame occur close enough to each other spa-tially that the their charge clouds significantly overlap, the event(s) are piled up. Theexcess charge from the overlapping cloud distorts the event energy (causing the re-ported event energy to be too high), and modifies the distribution of charge within the3 × 3 pixel event “island”, thus altering the event grade (“grade migration”). Grademigration tends to spread charge into more pixels, degrading the quality of the event;the frequency of grade 0 (single pixel) events decreases while that for grade 6 eventsincreases. In addition, events with ASCA “good” grades (grades 0,2,3,4,6) can be con-verted into ASCA “bad” grades (grades 1,5,7). If the event morphs into a sufficientlybad grade, it may end up in one of the grades outside the ASCA grade set; the eventmay be filtered out onboard in which case it does not appear in the telemetry stream.

Pileup thus affects the data by distorting the spectrum (making the spectrum ap-pear harder) and depressing the effective QE for the piled up events. The event rate isdecreased as merged events are reported as a single event. Pileup is mostly a concernfor bright point sources close to on-axis. The narrow PSF core results in photons re-peatedly landing in single pixels. As the telescope dithers, the aimpoint shifts by onlya small fraction (<∼1/3) of a pixel during the frame collection time. Pileup can also bea problem for sufficiently bright diffuse emission.

In the Her X-1 (ObsID 3662) observation, the source is bright enough that thefar core and near wings are piled up. (The core itself is so heavily piled up that ahole appears in the profile, even in the level 1 event list; most of the core events arefiltered out onboard.) The surface brightness for the on-axis PSF falls with increasingdistance from the core, so the degree of pileup also falls with distance from the core.The determination of pileup is important for understanding this observation: we needto know how far into the core the profile can be extended before pileup becomes anissue. A number of approaches for assessing pileup in the halo profile were examined.

Grade migration can provide a pileup diagnostic. Smith et al. (2002) looked at thegrade 0/grade 6 ratio as a pileup diagnostic for and observation of a bright source onthe ACIS-I array. This diagnostic will be examined below.

A. Vikhlinin7 suggested an approach estimating the QE suppression from pileup inthe limit of mild pileup: since each piled up event corresponds to at least two photonsthe QE suppression can be estimated to be at least 2 × g157/g02346 where g157 is thesum of the ASCA “bad” (1,5,7) grades and g02346 is the sum of the ASCA “good”(0,2,3,4,6) grades; particle background, which has a different grade distribution, mustalso be accounted for. This suggests that the “bad/good” ratio, g157/g02346, could alsobe used as a pileup indicator.

I plot in Fig. A.1 the bad/good ratio as a function of energy for X-ray events andfor particle background events. The values for X-ray events are based on ACIS-S3ground (subassembly) testing8. The good/bad ratio for background particle events isbased on blank sky background and “stowed” background level 1 datasets provided

7Internal memo.8http://cxc.harvard.edu/cal/Acis/Cal prods/branch/pre flight/pre flight.html

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by M. Markevitch9 The bad/good ratio for X-ray events is ∼ 1 − 2% at low energies,and gradually reaches ∼ 9% at high energies. In the background datasets, the ratio is∼ 10% at low energies, but rapidly climbs above ∼ 5 keV. This suggests that for softsources with emission mainly ≤ 5 keV, filtering the energy to E ≤ 5 keV would reducethe effect of background in deriving the bad/good (g157/g02346) ratio.

Figure A.1: Ratio of ASCA “bad” grades to ASCA “good” grades for ACIS-S3 sub-assembly data and ACIS-S3 on-orbit background data. The subassy dataare from subassembly calibration test during ground testing. The bg andbg stowed datasets are level 1 background datasets. bg is blank sky back-ground, and bg stowed is background taken when ACIS was out of thefocal plane and not exposed to the sky. See text.

In the case of Her X-1 the spectrum is very soft, with most of the emission below∼ 1 keV. For moderate pileup in the near wings, most of the detected piled up eventswill have energies less than ∼ 2 keV. Evaluating the grade ratio for energies between0.5 and 2 keV emphasizes the grade migration of X-ray events, while reducing thecontamination from the background events at higher energies.

In the left panel of Fig. A.2 the radial profiles of bad events and good events areplotted for the Her X-1 observation, and in the right panel the corresponding bad/goodratio is plotted. The profiles are based on the level 1 event list after filtering on energy(0.5 − 2.0 keV) to reduce the inclusion of particle events. In the left panel, the bad

9private communication.

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events dominate inside ∼ 2 − 3′′; at larger radii the bad events fall more rapidly thanthe good events. Beyond ∼ 100′′ the profile for the bad events levels off. The trendscan be seen more clearly in the ratio plot in the panel on the right. The rapid riseinside ∼ 15′′ indicates that pileup increases in importance and then dominates thedistribution. Inward of 2′′ the grade migration is severe and in the core, all events arelost. From ∼ 15′′ to ∼ 100′′ the profile is dominated by valid X-ray events with a lowbad/good ratio characteristic of the photons in the 0.5−2.0 keV band. Beyond ∼ 100′′

particle background is becoming important, which produces the upward trend in thebad/good ratio.

Figure A.2: Left: Her X-1 data. Surface brightness profiles for ASCA good grades andASCA bad grades. Status filtered and energy filtered 0.5 − 2.0 keV. Noexposure correction applied. Right: Her X-1 data: as in bottom left figure,but showing the ratio of ASCA bad grades to ASCA good grades.

I also examined other approaches to assessing pileup, and examined modified ver-sions of diagnostics used in Smith et al. (2002).

Grade migration for a source imaged on the ACIS-I array was examined in Smithet al. (2002); the behavior of the ratio of ASCA grade 0 to the sum of ASCA goodgrades (0, 2, 3, 4, 6), and the corresponding ratio for grade 6 seemed to provide a gooddiagnostic. With grade migration single-pixel events (grade 0) migrates to other grades,and particularly grade 6. The decrease of the grade 0 fraction and the the increase inthe grade 6 fraction toward the core of the image was taken as an indication of pileup;the grade fractions became asymptotically flat at large radii.

The Her X-1 ObsID 3662 images the source on the back-illuminated chip ACIS-S3,and the g0/g6 criterion is not as distinctive as for the FI chips; background makes amore significant contribution. I examined the grade fractions as a function of radius,

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and found that the grade 6 fraction decreases radially outward, reaches a minimum,then increases. Similarly, the grade 0 fraction increases, reaches a maximum, thendecreases. I examined grade ratios as a function of energy, and also examined graderatios for background datasets. The particle background has a significantly largerfraction of grade 6 events, particularly above ∼ 2 keV. As in the case of the “bad/good”ratio test discussed above, the peculiarity in the grade ratio profiles is a result of theincreasing importance of background events with increasing radius. Again, filtering onenergy (0.5−2.0 keV produces a cleaner evaluation of the diagnostic. The grade 6 andgrade 0 profiles are plotted in the left panel of Fig. A.3. This diagnostic suggests thatpileup is important inside ∼ 8′′.

Finally, a crude estimate can be made based on Poisson statistics (Smith et al.,2002). For the diffuse scattered emission, I estimate the source rate such that thereis a 5% probability that two events will land in a 3 × 3 pixel island within a singleframe (3.1 s for ObsID 3662). This is only approximate, since the diffuse emission isnot uniform. In the right panel of Fig. A.3, the radial profile for the Her X-1 ObsID3662 observation is plotted, and the Poisson-based pileup estimate is indicated as ahorizontal line. Moving radially inward, the profile peaks, then plummets to zero aspileup becomes extreme and all events are morphed into bad events. Based on thisdiagnostic, I estimate that pileup is becoming significant ∼ 8′′ from the source.

Figure A.3: Left: Profiles of the ratios of grades 0 and 6 to the sum of grades 0, 2, 3,4, and 6 for ObsID 3662. Right: Her X-1 ObsID 3662 surface brightnessprofile; the horizontal line indicates an estimate of the rate at which pileupis ∼ 5%.

Comparing the various pileup estimates, the “bad/good” ratio diagnostic is themost sensitive. I conclude that pileup is likely a significant factor inside ∼ 8′′, and

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possibly as far out as ∼ 15′′. To be conservative, the profiles are fit only for θ ≥ 15′′,but the extrapolated profile still fits reasonably well inward of 15′′.

B The ACIS Transfer Streak

At the Colorado HEAD meeting (Estes Park, 1997), M. Bautz suggested makinguse of the ACIS transfer smear during frame readout to allow photon counting forheavily piled up sources. The following describes how this can be used to estimate thesource rate for a heavily piled up point source.

ACIS accumulates events for a frame exposure time (EXPTIME, 3.1 s for this ob-servation), then rapidly reads out the frame with a parallel transfer rate of 40µs perrow; the parallel transfer time for a full frame is 0.04104 s (the difference between theTIMEDEL and EXPTIME values). Because there is no shutter, the CCD still accumulatesevents during the frame transfers; each pixel thus samples the source plus backgroundalong the whole column, accumulating charge as the packet is clocked over the sourcedistribution. Normally the transfer streak is not noticeable except in the case of brightpoint sources. In general, however, it affects every pixel in every column: ihe exposurefor each pixel includes a scaled-down sum of the source plus background for its column.

Any given pixel picks up part of its transfer-streak charge while being clocked inat the beginning of the frame (the portion closer to the frame store), and part whilebeing clocked out at the end of the frame (the portion further from the frame store).The transfer streak thus extends both directions from sources.

Because the frame accumulation time (≤ 3.2 s) is much shorter than the dithertimescale (∼ 103s), the projected sky position shifts by only a small fraction of a pixelduring a single frame. The transfer streak can be considered as effectively instanta-neous as far as dither is concerned, even though part of the transfer streak exposure isaccumulated at the beginning of a frame and part at the end of a frame.

B.1 Estimating the Transfer Streak Spectrum

To utilize the transfer streak:

• Extract a narrow region in the direction of the transfer but excluding regions nearthe core of the image where events are piled up (see Fig. B.1).

• Evaluate the source count rate in the transfer streak (number of events in thepixel/packet dwell time).

• Subtract a corresponding background count rate, scaled for the background ex-posure time and extraction area.

• Correct for the effective “duty cycle” for the frame transfer. The streak extractionarea is N pixels long, and the pixel dwell time for parallel transfer is 40µ s perpixel. The duty cycle is thus N × 40µ s/tframe where tframe is the frame collectiontime (3.1 s for the Her X-1 observation. Note that the background subtractionoccurs before correcting for the frame transfer duty cycle; almost all background

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events will have occurred during the frame collection rather than during theparallel transfer.

• In principle, a correction for PSF sampling in the transverse direction and contri-bution of the wings in the streak direction should also be applied. This has notbeen done at this time. The expected correction is smaller than other systematicuncertainties. Such corrections could be done as follows:

– evaluate the line PSF based on the core of the PSF and the width of thetransfer streak clipping region. The ACIS-S and ACIS-I arrays have differentclocking directions, so two versions of the correction factor will have to beevaluated.

– The contribution of the wings to the transfer streak can be evaluated byusing a fit to the wings from regions excluding the transfer streak.

Currently, these corrections are not applied.

B.2 Evaluating the Her X-1 Transfer Streak Spectrum

In the case of the Her X-1 observation, 15994 frames were accumulated (determinedfrom the number of unique EXPNO values). The streak spectrum is extracted from a10′′ wide region, 609 pixels in length, centered on the bright core of the transfer streak.The accumulated exposure time in the streak during frame transfer is 609×15994×4×10−5 = 389.614 s. Rates estimated from the spectrum need to be scaled by 127.298, theratio of observation exposure time (49579.136 s) to the effective streak exposure timefor the extracted streak spectrum (389.614 s); the inverse of this ratio is the effectiveduty cycle for frame transfer.

The rate for each energy range is determined by integrating over PI column inthe spectrum file, treating the distribution as a piecewise constant function of PI. Again correction is applied. In simultaneous fits to Chandra transfer streak data andRXTE data, Heinke et al. (2003) found they needed a shift in the slope of the gainfunction of 7%±1%. My fits to the Her X-1 (ObsID 3662) transfer streak data indicatea gain shift of ∼ 2.5%. Simultaneous fits to transfer streak data for an observationof 3C273 on ACIS-S3 without the grating (ObsID 1712) and MEG data for 3C273(ObsID 2463) suggest a gain slope offset of ∼ 3%. These estimates for the gain slopeshift are dominated by the shift in position of the Ir Mv edge at ∼ 2.1 keV; in theTerzan 5 data analyzed by Heinke et al. (2003) the statistics for this edge , and thereis significant flux in the region of overlap with the RXTE spectrum (E ≥ 3 keV).The reason for the larger slope shift obtained by Heinke et al. (2003) is not currentlyunderstood; a possibility is a calibration offset between the two observatories. In anyevent, the properties of the ACIS transfer streak spectrum needs to be studied moresystematically. Given the uncertainties, for the present analysis a linear slope shift of2.5% with no offset is used:

Ecorr = (1 + α)E (5)

where α = 1.025.

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PSF core

∆y

Transfer Direction

∆xFigure B.1: Schematic of the transfer streak calculation. ∆x should be large

enough to include the core and near wings, but small enough tominimize the enclosed background. ∆y should extend over a regionfar enough away from the source that the included wing profile issmall compared to the transfer streak contribution. A correspondingbox on the other side of the direct image can be added to improvethe statistics.

The background-subtracted rate in an energy bin ∆Ek is estimated as:

Sstreak (∆Ek ) ≃fxfr ,streak

ARF src,corr (∆Ek )

[

Cstreak (∆Ek )

texp,src−Cbgd(∆Ek )

texp,bgd

]

(cts s−1) (6)

where Cstreak (∆Ek ) the number of counts in the streak extraction region and Cbgd(∆Ek )is the number of counts for the same region in the background dataset; texp,src = 50ksis the exposure time for the Her X-1 wings observation, and texp,bgd = 350 ks is theexposure time for the blank sky background data. The ARF src,corr (∆Ek ) term is thevalue of the ARF (with a spatially independent correction for the ACIS contamination)summed over PI and averaged over a 10′′ radius circle centered on the Her X-1 specularimage. The correction used A. Vikhlinin’s corrarf with the qe cor.H20.C10.O2.N1

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contamination model, which is based on G. Chartas’ ACISABS corrector. The factor

fxfr ,streak =3.1 s

609 rows × 40µs /row= 127.298 (7)

is the inverse of the effective duty cycle for frame transfer through the streak extractionregion (609 rows in the parallel transfer direction).

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B.3 Pileup in the Her X-1 ACIS Transfer Streak

Alexey Vikhlinin (internal memo, 2004) suggested that QE depression from pileup(in the low pileup limit) can be estimated by comparing the ASCA “good” grades(grades 0, 2, 3, 4, and 6) to the ASCA “bad” grades (grades 1, 5, and 7). Since each badevent, if generated by pileup, corresponds to at least two photons, the ratio 2g157/g02346is an estimate for the minimum QE depression caused by pileup. (Background eventshave a different grade distribution than X-ray events, so the effect of background onthe estimate needs to be taken into account; see Appendix A.)

For the level 1 event list, a narrow region centered on the transfer streak is examined.The region is 4 pixels by 984 pixels, and a circular region 40 pixels in radius centeredon the specular image of Her X-1 is also excluded. The grade ratio for these eventsis g157/g02346 ≃ 0.039, implying an effective QE loss of ∼ 8%. The rate per frame inthe transfer streak is estimated by examining the statistics of counts within the region;The mean rate is 9.40 ± 3.85 cts/frame. A simple Poisson estimate based on at leastone additional photon hitting the location of a detected event or one pixel to eitherside (as the event is clocked through) is ∼ 4.1%. The pileup fraction for the transferstreak is thus estimated as ∼ 4%. The normalization factors for the Her X-1 profileshave been scaled by 1.08 to account for this effect.

C Exposure Correction and Effective Area

In principle, the effective area which should be used varies depending on the originof the event:

• For directly (i.e., specularly) imaged photons from astrophysical sources, Aeff

appropriate to the detected position should be used.

• For photons scattered by the mirrors (mirror scattering halo), the Aeff appropriateto the location of the specular image of the source should be used; the vignettingfunction implicitly includes the mirror scattering contribution.

• For particle background events Aeff should not be used since these are not imagedX-rays. If these events are subject to vignetted at all, the vignetting will be incompletely different way than for imaged X-rays.

• For ACIS transfer streak events, the Aeff appropriate to the location of the spec-ular image of the source should be used; the X-ray actually hit the the detectorat the direct image, and its detected position is an artifact. In general, it is notpossible identify likely transfer streak events unless there is a single bright sourcein the column.

In practice, it is not possible to distinguish reliably events resulting from mirror-scattered photons from particle background events or from directly imaged sky photonsfrom diffuse emission. Thus, it is not possible to apply a different Aeff depending onwhat produced the event, so compromises are needed. In any case, treatment of vi-gnetting for background events should be consistent with the treatment of the sourceevents.

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In this work, the correction for effective area and detector QE is done in two distinctways:

• For study of the mirror PSF properties, one wants to get to the intrinsic mirrorperformance. The deep wings observation provides good statistics so that themirror scattering wings generally dominate over the background. In this case,the effective area at the specularly imaged position of the source is used, ratherthan that associated with the detected position. The image is flattened usinga projected instrument QE map (incorporating the aspect solution but not theHRMA vignetting). The effective area (including vignetting) is instead evaluatedat the position of the specular image of Her X-1. For consistency, the flattening ofthe blank sky background data is done the same way. These results are reportedin §4.

• For studies of source extent or diffuse emission, the diffuse emission may be sig-nificant compared to the mirror scattering contribution. As noted above, it is notpossible to categorize events uniquely into events resulting from mirror scatter-ing, events resulting from diffuse astrophysical emission, and detector background.Typically, one might apply the mirror vignetting correction in the computationof the exposure map, even though it is not strictly applicable to those eventsresulting from mirror scattering or detector background. Again, for consistency,the flattening of the blank sky background would be done in the same way, eventhough the particle background component would not be vignetted in the sameway as X-ray events. For comparison, results applying this approach are reportedin Appendix D.

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D Fits Including Mirror Vignetting

Although the mirror vignetting function should not be applied to photons whichare scattered by the mirror, in some analyses it is necessary to do this. For studies ofsource extent or diffuse emission, the diffuse emission may not be negligible comparedto the mirror scattering contribution. It is generally not possible identify a givenevent unambiguously as a photon from a specular source scattered by the mirrors, aphoton from diffuse astrophysical emission (e.g., source extent, or a diffuse cosmic dustscattering halo), or a background particle event. If the analysis requires applying thevignetting function to the data, then vignetting would need to be applied to the mirrorscattering (and background) data.

In this appendix, an analysis is presented which includes the mirror vignetting inaddition to the detector QE when generating the exposure correction. For consistency,the exposure correction for the background data set now also includes the mirror vi-gnetting. The profiles are calculated as

〈ψsrc〉∆θi=

⟨

C ′

src,corr

⟩

∆θi

tsrc,exp(8)

where C ′

src,corr = Csrc,counts/Aeff qQ is the vignetting and QE-corrected counts image.The Aeff is now the effective area at the detected position, see §C; texp is the exposuretime, and q is a correction factor for the low-energy QE degradation at the time ofthe observation (very close to 1 for E>∼1). The 〈〉∆θi

again indicates an average overannulus i of width ∆θi . The surface brightness for background is constructed in thesame way using the sky background dataset:

〈ψbgd 〉∆θi=

⟨

C ′

bgd ,corr

⟩

∆θi

tbgd ,exp

(9)

where C ′

bgd ,corr = Cbgd ,counts/Aeff Q; The low-energy QE correction term, q, is notapplied.

The wing profile is fit by a powerlaw plus exponential cutoff plus spatially constantbackground:

ψ(θ) = a

[

θ

θ0

]

−α

exp (−cθ) + b (10)

where b is the background component, a is the wing amplitude scale factor, α is thepowerlaw slope, and 1/c is the exponential cutoff scale length. The fit is scaled to areference radius, θ0 ≡ 10′′. The background datasets are fit with the a parameter frozenat 0. The resulting fit parameters are shown in Table D.1, and the profiles plotted inFigs. D.1–D.4.

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Tab

leD

.1:

Fit

Par

amet

ers.

(Not

e:er

rors

are

pure

lyst

atis

tica

l.)

Ener

gyγ

ac

bχ

2(d

of)

(keV

)(c

ts−

1ar

csec

−2)

(arc

sec−

1)

(cts−

1ar

csec

−2)

1.0-

2.0

1.96

7±

0.00

3(0

.744

±0.

004)

×10

−05

(0.5

64±

0.04

9)×

10−

03

(0.3

91±

0.00

3)×

10−

08

221(

70)

2.0-

3.0

1.84

1±

0.00

4(1

.013

±0.

007)

×10

−05

(1.0

75±

0.06

0)×

10−

03

(0.5

47±

0.00

5)×

10−

08

87(7

0)3.

0-4.

01.

764±

0.00

8(1

.884

±0.

016)

×10

−05

(1.8

36±

0.05

2)×

10−

03

(0.6

83±

0.00

7)×

10−

08

132(

70)

4.0-

5.0

1.75

7±

0.00

8(2

.591

±0.

022)

×10

−05

(1.8

23±

0.05

1)×

10−

03

(0.8

72±

0.00

9)×

10−

08

81(7

0)5.

0-6.

01.

924±

0.01

1(3

.533

±0.

038)

×10

−05

(1.4

73±

0.07

4)×

10−

03

(1.4

87±

0.01

5)×

10−

08

153(

70)

6.0-

7.0

2.00

2±

0.01

6(4

.166

±0.

061)

×10

−05

(1.0

57±

0.11

7)×

10−

03

(3.5

30±

0.03

3)×

10−

08

164(

70)

7.0-

8.0

2.26

4±

0.03

2(5

.303

±0.

139)

×10

−05

(2.0

31±

0.25

5)×

10−

03

(18.

425±

0.13

1)×

10−

08

269(

70)

32 / 44

Chandra PSF Wings

Figure D.1: Powerlaw plus exponential cutoff fits to the obsid 3662 (Her X-1 wings)data; the fits were for θ ≥ 15′′. Mirror vignetting was included in exposurecorrecting the data (see text). The model based on ground calibration datais also indicated (labeled “xrcf”). Top: 1.0-2.0 keV. Bottom: 2.0-3.0 keV.

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Figure D.2: Powerlaw plus exponential cutoff fits to the obsid 3662 (Her X-1 wings)data; the fits were for θ ≥ 15′′. Mirror vignetting was included in exposurecorrecting the data (see text). The model based on ground calibration datais also indicated (labeled “xrcf”). Top: 3.0-4.0 keV. Bottom: 4.0-5.0 keV.

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Chandra PSF Wings

Figure D.3: Powerlaw plus exponential cutoff fits to the obsid 3662 (Her X-1 wings)data; the fits were for θ ≥ 15′′. Mirror vignetting was included in exposurecorrecting the data (see text). The model based on ground calibration datais also indicated (labeled “xrcf”). Top: 5.0-6.0 keV. Bottom: 6.0-7.0 keV.

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Figure D.4: Powerlaw plus exponential cutoff fits to the obsid 3662 (Her X-1 wings)data; the fits were for θ ≥ 15′′. Mirror vignetting was included in exposurecorrecting the data (see text). The model based on ground calibration datais also indicated (labeled “xrcf”).

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Figure D.5: Variation in local powerlaw slope. The curves are labeled by the value ofθ in arcsec. The highest energy band (7–8 keV) is poorly constrained; theoverall flatter profile and the extreme flattening seen at large radii likelyreflect problems with background subtraction.

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E Diffuse PSF Wings: spectral variations

The mirror scattering is in part diffractive, and the scattering angle depends onthe incident X-ray energy. In Fig. E.1, the spectrum extracted from the bright core ofthe transfer streak (extraction width 10′′) is plotted for reference. In Figs. E.2– E.4the spectra for the diffuse mirror scattering emission are shown for annular extractionregions between 10′′ and 400′′. The annuli exclude a narrow 16 pixel wide strip centeredon the bright core of the ACIS transfer streak, and also any regions falling off the ACIS-S3 detector (allowing for dither).

In the following figures, the spectral variation with E is particularly evident in thestructure for E<∼2 keV.

Figure E.1: Spectrum for the bright core of the Her X-1 transfer streak. Left: topcurve: streak spectrum; bottom curve: spectrum extracted from the cor-responding region of the blanks sky data. Right: background-subtractedtransfer streak spectrum. .

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Figure E.2: Spectrum of the Her X-1 diffuse mirror scattering wings (excluding thecore ACIS transfer streak). Top Left: 10′′ − 15′′; source and blank sky.Top Right: 15′′ − 20′′; source and blank sky. Bottom Left: 20′′ − 30′′;source and blank sky. Bottom Right: 30′′ − 40′′; source and blank sky.

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Figure E.3: Spectrum of the Her X-1 diffuse mirror scattering wings (excluding thecore ACIS transfer streak). Top Left: 40′′ − 60′′; source and blank sky.Top Right: 60′′ − 80′′; source and blank sky. Bottom Left: 80′′ − 120′′;source and blank sky. Bottom Right: 120′′ − 160′′; source and blank sky.

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Figure E.4: Spectrum of the Her X-1 diffuse mirror scattering wings (excluding thecore ACIS transfer streak). Top Left: 160′′ − 220′′; source and blank sky.Top Right: 220′′ − 280′′; source and blank sky. Bottom Left: 280′′ − 340′′;source and blank sky. Bottom Right: 340′′ − 400′′; source and blank sky.

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Figure E.5: Comparison of spectra for diffuse mirror scattering wing emission. Thespectra extracted for annuli are normalized by a spectrum extracted fromthe transfer streak. The legend indicates the annular angles in arcsec. Seethe text for discussion. .

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F Anomalous 1.5 keV line feature

For an initial investigation of the wings profile as a function of energy, a simplepowerlaw fit was performed for the very narrow band X-ray image data (Fig. F.1).

??

Steeper at low E

Roughest mirror drops out

Figure F.1: Powerlaw index for fits to the narrow band obsid 3662 data.

The glitch at 1.5 keV deserves comment. There is no reason why the profile slopeshould be discontinuous at that energy. A possible explanation was revealed by exam-ination of spectra of diffuse emission extracted from annular regions centered on thesource. For radii beyond ∼ 2′, the spectra show a pronounced line feature just below1.5 keV (see Fig. F.2, left panel). This is not a feature in the Her X-1 spectrum — itdoes not appear in the transfer streak spectrum (see Fig. F.2, right panel). We believethis to be an artifact, since it is not evident in the sky background data, nor in theHer X-1 transfer streak data. Based on energy, it is tentatively identified as an Al Kαfluorescence feature, but there is no obvious source for the emission. The aluminumsupport struts in the central aperture plate are illuminated by Her X-1 and are in theview of the focal plane but the very small solid angle subtended by the detectors wouldseem to make this unlikely. Similarly, there is some aluminum in the optical blockingfilter which is closer to the detector, but the aluminum is very thin (only ∼ 1300 A)so again it seems unlikely given the small optical depth and low fluorescent yield ofaluminum. For now, we exclude the 1.4-1.6 keV band from the analysis of the obsid3662 data and interpolate from the neighboring bands.

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Figure F.2: Top: Spectrum for the transfer streak of Her X-1 (obsid 3662). Frametransfer is effectively a different ACIS mode, and it has not been calibrated.There is a shift in the slope of the gain of at least a few percent; this canbe seen clearly at the Ir M edge just above 2 keV. (The rate has not beencorrected for the effective transfer streak duty cycle.) Bottom: Spectrumfor Her X-1 (obsid 3662) for an annular region 160–220′′ from the source.In both panels, the upper curve is the Her X-1 obsid 3662 data. The lowercurve shows the spectra for the corresponding blank sky data.

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